A linear programming computer package is needed.

Greenville Cabinets received a contract to produce cabinets for a major furniture distributor. The contract calls for the production of $3,300$ small cabinets and $4,100$ large over the next two months, with the following delivery schedule

Model Month $1$ Month $2$

Small $2,1001,200$

Large $1,5002,600$

Greenville estimates that the production time for each small cabinet is $0\mathrm{.}7$ hours and the production time for each large cabinet is $1$ hour. The raw material costs are $$10$ for each small cabinet and $$12$ for each large cabinet. Labor costs are $$22$ per hour using regular production time and $$33$ using overtime. Greenville has up to $2,400$ hours of regular production time available each month and up to $1,000$ additional hours of overtime available each month. If production for either cabinet exceeds demand in month $1,$ the cabinets can be stored at a cost of $$5$ per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. $($Round your answers to the nearest integer. Let SaR $=$ regular small cabinets for month $1,$ SbR $=$ regular small cabinets for month $2,$ LaR $=$ regular large cabinets for month $1,$ LbR $=$ regular large cabinets for month $2,$ SaO $=$ overtime small cabinets for month $1,$ SbO $=$ overtime small cabinets for month $2,$ LaO $=$ overtime large cabinets for month $1,$ and LbO $=$ overtime large cabinets for month $2)$

$($SaR$,$ SbR$,$ LaR, LbR$,$ SaO, SbO, LaO, LbO$)=$

Total Production Cost $=$ $